 # NCERT Solution for Class 8 Maths Rational Numbers ## NCERT Solution for Class 8 Maths Rational Numbers

Class 8 Maths Rational Numbers : In mathematics, we usually come across different terms like natural number, whole numbers, integers and rational number. We will discuss rational number in this article from  8 Class Maths.

Let’s us revisit the properties of Rational numbers in class 8.

Rational Numbers

A rational number is a number that can be written in the form of P/Q where P and Q are integers and Q is not equal to 0.

Example:-5/7, (-2/3)

Properties of Rational numbers

We will first discuss the properties of rational numbers.

Closure Property

We call a set of numbers closed under operation if performance of that operation on members of the set of numbers always creates a member of the same set only; in this case we also say that the set is closed under the operation.

Rational numbers are closed under addition.For any two rational numbers a and b,a+b is also a rational number.

Under subtraction

Rational numbers are closed under addition.For any two rational numbersaand b, a-b is also a rational number.

Under Multiplication

Rational statistics are closed under multiplication.For any two rational numbers a and b, a*b is also a rational number.

Under Division

Rational numbers are not closed under multiplication.For any rational number a, a/0 is not defined.

Commutative Property

As per commutative property, the interchanging order of numbers will not change the result.

Two rational numbers can be added in any order.Addition is commutative for rational numbers.For any two rational numbers a and b, a+b=b+a

Under subtraction

Subtraction is not commutative for rational numbers.

Under Multiplication

Multiplication is commutative for rational numbers. For any two rational numbers a and b, a*b=b*a

Under Division

Division is not commutative for rational numbers

Associative Property

Addition is associative for rational numbers.For any 3 rational numbers a,b, and c.

a + (b+c) = (a+b) +c

Under subtraction

Subtraction is not associative for rational numbers

Under Multiplication

Multiplication is associative for rational numbers.For any 3 rational numbers a,b, and c.

a *(b * c) = (a * b) *c

Under Division

Division is not associative for rational numbers.

For illustrations and solved NCERT solutions, visit Class 8 NCERT Maths solutions

The Role of Zero

Zero is called the identity for the addition of rational numbers.It is the additive identity for integers and whole numbers as well.

a+0=0+a=a

b+0=0+b=b

The role of 1

1 is the multiplicative identity of rational numbers.

a*1=1*a=a

Negative of a number

For any rational number a/b, we have a/b+(-a/b)=(-a/b)+a/b=0.We say that (-a/b) is the additive inverse of a/b and a/b is the additive inverse of (-a/b).

Reciprocal

A rational number c/d is called the reciprocal or multiplicative inverse of another rational number a/b, if a/b*c/d=1.

Distributive property of multiplication over addition and subtraction

For all rational numbers a,b, and c

a (b+c)=ab+ ac

a(b-c)=ab-ac

Rational Numbers between two rational numbers

Let’s consider the below example for 8th class maths

Q – Find rational number -1/10 and 3/10?

Sol- Rational numbers -1/10 and 3/10 are

0/10,1/10/2/10

For Class 8 Maths NCERT solutions, CBSE Guide, sample papers for exam preparation, online classes  for school courses, register with Takshila Learning.

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August 17, 2017

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